Question
Train 'K' leaves at 6:00 PM on Saturday from Ahmedabad
station and reaches Surat station at 8:00 AM the next day, while train 'L' leaves at 7:00 PM on Saturday from Surat station and reaches Ahmedabad station at 9:00 AM the next day. Find the time at which the two trains meet each other.Solution
ATQ, Let the speed of the train 'K' and train 'L' be 'x' km/h, and 'y' km/h, respectively. For train 'K', from 6:00 PM to 8:00 AM next day: Total time = 14 hours Similarly, for train 'L' From 7:00 PM to 9:00 AM next day: Total time = 14 hours ATQ: Total distance between Ahmedabad and Surat = 14 X x = 14 X y Or, (x/y) = (14/14) Or, (x/y) = (1/1) Therefore, x = 1:1 Let the speed of train 'K' and train 'L' be 'a' km/h, and 'a' km/h, respectively. Distance travelled by train 'K' in 60 minutes = a X (60/60) = 'a' km Remaining distance between train 'K' and train 'L' when train 'L' started = 14 X a - 'a' = 13a km We know that, When two objects moving in opposite direction, then their relative speed = Sum of their individual speed Required time taken to meet = 13a / 2a = 6.5 hrs Time at which the trains will meet = 6.5 hours after train 'L' started = 1:30 AM next day
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